The global positioning system (GPS) is a satellite-based radio navigation system. In the GPS system, each GPS satellite, also called “space vehicle” (SV), broadcasts time-tagged ranging signals and navigation data. A GPS receiver tracks the satellites whose signals are within its field of view. From these visible satellites, a GPS receiver extracts the navigation data and obtains range measurements from its received GPS satellite signals. The range measurements are used in a navigation solution to calculate a position fix of the GPS receiver.
The GPS navigation data contain, but are not limited to, satellite ephemeris, where ephemeris parameters can be used to accurately calculate satellite position and velocity. In addition to knowing the satellite position, the GPS receiver receives the range measurement to the satellite in order to calculate the position fix. Range measurements include, but are not limited to, two types of measurements—pseudorange (PR) and delta range (DR).
A pseudorange is the apparent distance from the GPS receiver to the satellite. It is calculated by multiplying the speed of light by the apparent transit time, which is the time difference between a signal reception time based on a receiver clock and a signal transmission time based on a satellite clock. This range is termed pseudorange since the receiver clock is not synchronized with the satellite clock and thus the measured range is not necessarily the true range.
A second type of range measurement that is used to calculate the position (including velocity) fix is the DR. DR is a range change rate in unit of meters per second or Doppler. Doppler measurement is a function of a relative velocity, and a relative frequency clock drift between the satellite and the GPS receiver. Accumulated DR (ADR) measurement is also called carrier phase measurement or integrated Doppler measurements in the GPS field. The Doppler or DR measurement allows the receiver to calculate a receiver velocity and a receiver frequency clock drift rate, from which a new position fix can then be obtained if a previous position is known.
To achieve accuracy and integrity, the GPS receiver typically includes algorithms that contain some failure detection and exclusion (FDE) functions to detect and exclude failed range measurements. GPS measurements can be affected by multipath signals, where the GPS signals reflect off, for example, surrounding terrain, buildings, canyon walls, and hard ground, among others. When a signal is reflected, the signal typically passes through a longer path than the corresponding direct-path signal. Thus, the multipath signal can affect the pseudorange measurements, resulting in potential unexpected positive or negative errors. When direct-path signal is blocked, then multipath can make pseudorange measurements erroneously longer. Accordingly, pseudorange residuals, also known as, innovations or errors, can be referred to as a pseudorange measurement minus an estimated range. Many FDE functions can determine whether the pseudorange measurements are normal or failures based typically on the magnitude of the pseudorange residuals. It should be noted that since one pseudorange measurement is typically converted to a corresponding pseudorange residual in navigation algorithms, these two terms sometimes can be exchanged. For example, processing pseudorange measurement residual has the same meaning as processing pseudorange measurement. The two terms will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description.
A large pseudorange residual typically indicates a failure or a potential failure. The FDE function can either exclude or de-weight the failed measurements in the navigation computation. However, the FDE algorithms have a certain probability of false alarms (Pfa), such as, for example, mistakenly excluding good measurements, and a certain probability of misdetections (Pmd), such as, for example, failing to detect bad measurements. Excluding measurements can adversely affect satellite geometry distribution or, in other words, dilution of position (DOP), which, in turn, can magnify measurement errors into position solution errors. In addition, excluding a pseudorange measurement among only three or four available pseudorange measurements can reduce GPS availability.
As mentioned above, many FDE algorithms determine the quality of a measurement based on its corresponding residual, which is the measurement minus an estimated measurement. However, an estimated range is the distance between a satellite position, which can be precisely computed based on its ephemeris, and a receiver position, which generally refers to a GPS fix. However, in tough environments and/or in any cases when a receiver previously performed badly, the previous GPS fix of the receiver position can be inaccurate as well as the estimated range residuals. In other words, range residuals are calculated based on previously estimated receiver position, and therefore the accuracy of range residuals also depends on the accuracy of GPS position fixes. In addition, though many FDE algorithms are effective in detecting spike errors, they are not effective in detecting slow-change errors.